Mpemba effect
The Mpemba effect describes the phenomenon in which, under suitable conditions, previously hot water freezes faster than previously cold water. The effect was named after its "rediscoverer" (1963), the Tanzanian student Erasto B. Mpemba , who made the effect internationally known through a publication in 1969.
definition
If the same initial quantities of warm and cold water are cooled in the same vessels under the same pressure and the same ambient conditions to a temperature that corresponds to the freezing point of water at this pressure (0 ° C or 273.15 K at a pressure of 101.325 kPa), so it can be observed in a certain range of starting temperatures and cooling rates that the water warmer at the beginning of the experiment freezes faster than the originally cooler water. This paradoxical phenomenon is known as the Mpemba effect. In the literature, however, there are at least three different definitions of what exactly is called the Mpemba effect: It can refer to the time until the temperature reaches 0 ° C; then the Mpemba effect consists of faster cooling down to this temperature. Other authors, e.g. B. Mpemba himself, consider the beginning of freezing as a decisive criterion, others (e.g.) complete freezing.
history
Already in the fourth century BC, the philosopher Aristotle reported about faster freezing of warmed water as an example of the antiperistasis he postulated ( ancient Greek ἀντιπερίστασις ), according to which one quality increases when it is surrounded by an opposing one:
“It also contributes to the speed of freezing if the water is warmed up beforehand; then it cools down faster. That is why many people first put water in the sun that they want to cool down quickly, and when the inhabitants of the Pontus area set up their huts for fishing on the ice (they punch a hole in the ice and fish), then they pour hot water on their fishing rods to freeze them faster; they use ice instead of lead to immobilize the rods. "
In the 13th century this was discussed by the monk and philosopher Roger Bacon ( Opus Majus 6.1).
In the 17th century, the philosophers and scientists Francis Bacon ( Novum Organum 2.50) and René Descartes ( Les météores 1) mentioned the effect.
In 1775 a work by the Scottish scientist Joseph Black appeared in which he ensured the effect on the basis of experiments.
In 1788, the first German professor of experimental physics, Georg Christoph Lichtenberg, noticed such a process in his own experiments, but was unable to reliably reproduce it.
In 1963, the Tanzanian student Erasto B. Mpemba encountered the phenomenon while making ice cream . Together with Denis G. Osborne he published the results of numerous experiments on this subject in 1969. However, it took a few years before the effect was further scientifically investigated.
root cause
The cause of this paradox has not yet been fully scientifically explained. However, there are hypotheses which, on the one hand, see the main cause in the fact that the amount of warmer water when cooling in an open system through evaporation decreases disproportionately compared to the amount of cooler water. This is because the vapor pressure of a liquid (to which in turn the rate of evaporation is proportional) increases exponentially with temperature. This means that in relation to the same unit of time, more hot than cold water evaporates ( August's vapor pressure formula ). As a result, if open vessels are used in the experiment, different amounts of water are present when the freezing point is reached, in such a way that the amount of the originally warmer water is smaller than the amount of the originally cooler water, and a smaller amount of water always freezes under otherwise identical conditions faster than a larger amount of water. In Jugend-Forscht experiments with closed vessels, the Mpemba effect occurred under otherwise identical boundary conditions but with a comparable frequency, which speaks against evaporation as the main cause.
On the other hand, there is the hypothesis that salts dissolved in water (especially hydrogen carbonates ) precipitate at high temperatures (e.g. as carbonates ) and thus no longer have any influence on the freezing point. In cold water, the concentration of the salts increases in the water that is still liquid after the start of crystallization. This leads to a lowering of the freezing point . But even in tests with desalinated water, the Mpemba effect occurred about as often under otherwise identical boundary conditions, so that dissolved salts cannot be the main cause.
Recent experiments indicate that gases dissolved in the water or better heat circulation or dissipation in hot water can play an essential role. It is possible that the Mpemba effect occurs much less often than some experimenters believe: hypothermic samples, in which only a thin layer of water on the vessel walls has actually solidified to ice, can look deceptively similar to completely frozen samples and are therefore easily assigned incorrectly.
So far there is no agreement in the scientific discussion about which effects have the essential influence on the Mpemba effect under special experimental conditions. This is still controversial today and, also due to the sparse data material, some of which have methodological deficiencies, cannot yet be answered clearly.
Mpemba effect and thermodynamic systems
Open system
The Mpemba effect can be explained relatively easily if there is an open physical system . A possible exchange of substances and heat between the system and its environment is characteristic of open systems, whereby in the case of an open system the environment is by definition not included in the mass and energy balance of the overall system (or in other words: the environment is not a relevant part of the open system). Example: The water evaporating from an open beaker escapes into the atmosphere. As a result, both the amount of water in the glass and the amount of heat contained in the water decrease, while the water and energy content of the atmosphere increases at the same time. However, this increase is not taken into account or quantified, since the energy emitted is negligibly small relative to the energy in the atmosphere.
From a thermodynamic point of view, experiments in open systems change several intensive (mass-independent) and extensive (mass-dependent) quantities at the same time, which naturally makes the measurement and interpretation of observed effects more difficult.
Essential influencing parameters
The initial absolute amounts of water
These must not be too small so that the water does not evaporate completely before it has reached freezing point.
The initial absolute temperatures of the respective amounts of water
A large temperature difference between warmer and colder water promotes the Mpemba effect by allowing disproportionately more warmer water to evaporate. However, the temperature of the cooler water must not be too close to the freezing point, otherwise the hotter system will not have the opportunity to "overtake" the cooler one when it cools down.
The surface of the water
The size of the phase interface between the liquid and gaseous phase determines the amount of water that evaporates per unit of time (evaporation rate), as this is proportional to the size of the surface, provided the water is not boiling. The surface area in turn depends on the shape of the vessel. A large surface area, which leads to a high loss of substance through evaporation, is beneficial for observing the Mpemba effect.
The ambient temperature or the temperature of the so-called heat reservoir
The absolute temperature difference between the initial amounts of water and the reservoir determines the course of the cooling curve. The greater the difference, the steeper the cooling curves, i.e. H. the faster the samples cool down solely through thermal conduction and thermal radiation and the lower the loss of substance through evaporation. A temperature of the reservoir just below the freezing point of water is therefore favorable for observing the Mpemba effect, as the reservoir temperature is on the one hand low enough for the crystallization of the liquid water, on the other hand the cooling curves of the liquid phases are sufficiently flat and a maximum amount of water can evaporate during the cooling of the liquid phases.
The coefficient of thermal conductivity of the vessel
This determines the extent to which the water can be cooled via the vessel wall. The larger the coefficient, the faster the water cools down through heat dissipation and heat radiation through the vessel. For observing the Mpemba effect, a low thermal conductivity coefficient of the vessel is beneficial because more water can then evaporate during the cooling of the liquid phases; on the other hand, too low a thermal conductivity coefficient makes it more difficult to dissipate the heat of crystallization through the vessel wall during freezing, which again reduces the effect . In the practical experiment, for example, insulating vessels should not be used.
Scientific experiments are still required to determine whether and to what extent the Mpemba effect achieves its paradoxical result in the same or a comparable way when the two filled containers are at sea level or e.g. B. at an altitude of 7000 meters and / or they are set up at 45 degrees north latitude or at one of the two poles. The boiling point and also the freezing point in degrees Celsius or the associated pressure of the air column at the point of measurement include, among other things. a. most likely to the "determining conditions" for the measurement result. The test series could lead to a break-even point, at which point the paradox resolves and both water samples regularly freeze at the same time.
Disturbance parameters
The following parameters are not decisive for the occurrence of the Mpemba effect, although they can disturb it in an intensifying (positive) or weakening (negative) form. Therefore, they should be eliminated from the outset by a suitable choice of conditions when considering. Under special experimental conditions, however, a non-negligible contribution of these effects to the Mpemba effect is discussed.
Supercooled liquids or melts
If very pure liquids are cooled below their freezing point, crystallization may not occur if there are no crystallization nuclei in the liquid. To avoid this, a few grains of quartz sand can be added to the water samples as a crystallization matrix. Contrary to popular belief, the concentration (i.e. amount) of crystal nuclei is meaningless for any crystallization process, the only decisive factor is whether or not there is at least one suitable crystal nucleus. Incidentally, the lowering of the freezing point due to a lack of crystallization is independent of the fact that the freezing point of a liquid can shift to both lower and higher values depending on the pressure and volume of the system (see: phase diagrams of one-component systems).
In principle, the effect of the supercooled liquid has no effect on the Mpemba effect due to the lack of crystallization nuclei, since it affects the originally cooler sample as well as the originally warmer one. If one assumes, however, that the originally warmer water loses potential crystallization nuclei - for example through outgassing of dissolved foreign components such as carbon dioxide - in comparison to the originally cooler water, the effect of the supercooled liquids would weaken the Mpemba effect, since the formerly hotter water is now just not would freeze faster, but was prone to hypothermia.
Temperature gradients
Temperature differences in the system are also indicated by temperature gradients . In a stationary liquid, temperature differences occur during cooling as well as in the stationary environment. For example, the temperature on the vessel walls and at the phase boundary is lower than in the interior of the phase; in the surroundings the temperature is higher near the vessels than further away from them. In starting vessels of different warmth, different gradients occur during cooling, which are practically synonymous with a change in the thermal conductivity coefficient of the vessel. This effect is avoided by stirring the liquids (e.g. magnetic stirrer ) during cooling and a fan in the reservoir, which ensures a constant and uniform reservoir temperature.
Dissolved foreign matter
Dissolved substances (this also includes dissolved gases) can lower the freezing point of a liquid ( Raoult's law ), whereby the lowering of the freezing point is proportional to the amount of foreign matter. In the case of dissolved gases (e.g. carbon dioxide in water), the concentration of dissolved gas is again temperature-dependent (vapor pressure!), I.e. the water samples of different temperatures contain different amounts of dissolved gases under equilibrium conditions and therefore also have a slightly different freezing point. The effect is, however, very small (in the range from 0.01 K to 0.001 K) and therefore practically does not play a role in the Mpemba effect. The influence of dissolved gases would intensify the Mpemba effect, as the initially hotter water would contain fewer dissolved foreign components and therefore its freezing point would be less reduced compared to the initially cooler water. Overall, this “dirty effect” is avoided by using degassed water for the experiment (by boiling it beforehand and applying a vacuum). The same also applies to volume effects and other effects that could be caused by freezing gas bubbles.
Other parameters
Water vapor partial pressure
The water vapor partial pressure in the gaseous phase must be small compared to the saturation vapor pressure , since otherwise no or less water can evaporate. This condition is usually guaranteed when the test is carried out in a dry environment. A high water vapor partial pressure in the gaseous phase of an open system would weaken the Mpemba effect.
Influential parameters
Pressure dependence of the freezing point
The exact freezing point of pure water, like any liquid or melt, is pressure-dependent. The exact value can be taken from the so-called phase diagram of the water. At normal pressure (p = 1013.25 hPa) the freezing point corresponds to T = 0.000 ° C or T = 273.150 K. The freezing point of the water is at the condition p = 611.657 Pa (approx. 6 hPa) at T = 0.010 ° C or T = 273.160 K. At other pressures the freezing point can be above or below this value for the freezing point. This fact is independent of lowering of the freezing point due to dissolved foreign constituents and supercooled melts due to the lack of crystallization nuclei.
Microscopic structure of the liquid
The Mpemba effect can be fully explained in terms of classical thermodynamics. Microscopic properties such as the structure of liquids, apart from their importance for the caloric data of the substance under consideration, have no influence.
Other liquids
If the Mpemba effect is due to evaporation effects, it is not restricted to water (i.e. not an anomaly of the water). In this case, whether it occurs is mainly determined by the caloric data of a substance. Other substances such as ethanol , acetic acid , benzene or hexane show a similar exponential dependence of the vapor pressure on the temperature. However, the freezing points of these substances are either significantly lower than those of water, so that the practical experiment places higher experimental demands on the necessary cooling, or they are toxic or flammable, so that evaporation in open systems without special protective measures is prohibited.
Use of the Mpemba effect
According to Mpemba, the effect was used in the production of ice cream. If the ingredients have to be heated for homogenization and preservation ( pasteurization ) anyway, it does not matter that exploiting the effect has serious disadvantages compared to direct cooling: Heating and cooling require significantly more energy and take significantly longer than that cooling alone.
Conclusion
The result of the Mpemba effect is a surprising and counterintuitive visual effect. A physico-chemical basis of this is the evaporation of part of the liquid.
The consideration of the effect is suitable to train and deepen the knowledge of the principles of classical thermodynamics by means of a vivid and astounding experiment in the real world.
Mention in the media
On March 28, 1999, the Mpemba effect was clearly demonstrated and explained in the ARD science program Kopfball .
In the Sat.1 infotainment television program Clever! - The show that creates knowledge of March 13, 2006 (broadcast 39) was the Mpemba effect by cooling different, undefined initial amounts of water of different, undefined composition (mineral water, distilled water, tap water) and different temperatures in an open system demonstrated. As could be seen, the test setup and implementation were carried out under largely undefined initial and final conditions. The explanation of the effect given in the broadcast is incorrect.
On January 21, 2010, the WDR reported in Die Kleinefrage as part of the Leonardo radio show about the Mpemba effect, with some original sounds from Mpemba being recorded.
On June 26, 2012, the London Royal Society of Chemistry offered 1000 British pounds to help further explain the effect. Nikola Bregovic, chemist at the University of Zagreb , was announced as the winner in January 2013: he had come to the conclusion that he too could not find a final solution and stated: “Once again this small, simple molecule surprises and fascinates us with its magic. "
literature
Two articles by the same author in English with numerous sources, also on historical authors such as Aristotle, Bacon, Descartes:
- Can hot water freeze faster than cold water? by M. Jeng
- Monwhea Jeng: The Mpemba effect: When can hot water freeze faster than cold? In: American Journal of Physics . tape 74 , no. 6 , 2006, p. 514-522 , doi : 10.1119 / 1.2186331 , arxiv : physics / 0512262 .
- James D. Brownridge: A search for the Mpemba effect: When hot water freezes faster then cold water . March 16, 2010, arxiv : 1003.3185 .
Web links
- The Mpemba Effect. In: Wissenschaft-technik-ethik.de
- Why hot water turns to ice faster than cold water. In: Wissenschaft.de
Individual evidence
- ↑ a b Erasto B. Mpemba, Denis G. Osborne: Cool? In: Institute of Physics IOP (Ed.): Physics Education . tape 4 , no. 3 . IOP Publishing, May 1, 1969, ISSN 1361-6552 , pp. 172-175 , doi : 10.1088 / 0031-9120 / 4/3/312 ( iop.org ).
- ↑ a b c d e f Julian Schneider: The Mpemba effect and its cause . Investigations on temperature stratification and flow behavior in freezing water samples. In: Physikalisch-Technische Bundesanstalt PTB (Hrsg.): JungeWwissenschaft . Young people research nature and technology. tape 110 . Verlag Junge Wissenschaft, Düsseldorf 2016, p. 58–69 ( ptb.de [PDF; 1.3 MB ; accessed on June 14, 2019] Junge Wissenschaft No. 110 online ).
- ↑ a b Kathrin Passig, Aleks Scholz: Lexicon of ignorance: to which there has been no answer so far . Rowohlt-Taschenbuch-Verlag rororo, Reinbek near Hamburg 2008, ISBN 978-3-499-62230-4 , Wasser, p. 239-242 .
- ^ A b Paul F. Linden, Henry C. Burridge: Questioning the Mpemba effect: hot water does not cool more quickly than cold . In: Scientific Reports . tape 6 . Springer Nature, nature.com, November 24, 2016, ISSN 2045-2322 , p. 37665 , doi : 10.1038 / srep37665 ( nature.com ).
- ^ A b David Auerbach: Supercooling and the Mpemba effect: When hot water freezes quicker than cold . In: American Association of Physics Teachers (Ed.): American Journal of Physics . tape 63 , no. 10 . AIP Publishing, October 1995, ISSN 0002-9505 , p. 882-885 , doi : 10.1119 / 1.18059 ( robot-tag.com [PDF]).
- ↑ Julius Ludwig Ideler (Ed.): Άριστοτέλους μετεωρολογικά . Aristotelis meteorologicorum . Volume 1, Friedrich Christian Wilhelm Vogel, Leipzig 1834, p. 44 (Greek with Latin translation); Ernst Grumach , Hellmut Flashar (eds.): Meteorologie / Über die Welt , Aristoteles Werke 12.1./2., 3rd edition, Akademie-Verlag, Berlin 1984, p. 30 (German translation by Hans Strohm )
- ^ John Henry Bridges (Ed.): The 'Opus Majus' of Roger Bacon Volume 2, Clarendon, Oxford 1897, p. 169 (Latin); The Opus Majus of Roger Bacon Volume 2, Russell & Russell, New York 1962, p. 584 (English translation by Robert Belle Burke)
- ↑ Instauratio magna with Novum Organum , John Bill, London 1620, p. 345 (Latin); Franz Baco's Neues Organon , L. Heimann, Berlin 1870, p. 370 (German translation by JH v. Kirchmann )
- ↑ Discours de la méthode . La dioptrique. Les météores. La géométrie , Ian Maire, Leiden 1637, p. 164 (French); Discourse on Method, Optics, Geometry, and Meteorology , Hackett, Indianapolis 2001, p. 268 (English translation by Paul J. Olscamp)
- ↑ Joseph Black: The Supposed Effect of Boiling upon Water, in Disposing It to Freeze More Readily, Ascertained by Experiments. By Joseph Black, MD Professor of Chemistry at Edinburgh, in a Letter to Sir John Pringle, Bart. PRS . In: Philosophical Transactions of the Royal Society of London . 65, Jan. 1, 1775, pp. 124-128. doi : 10.1098 / rstl.1775.0014 .
- ↑ Ludw. Christian Lichtenberg , Friedrich Kries (eds.): G. Ch. Lichtenberg's mixed writings Volume 7, Ignaz Klang, Vienna 1844, p. 164 ; with reference to the article ice in Johann Samuel Traugott Gehler : Physical Dictionary Volume 1, Schwickert, Leipzig 1787, p. 676
- ^ The Mpemba Effect: A brief history. ( Memento of the original from June 3, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Royal Society of Chemistry, 2013
- ↑ Philipp Nagels: Mpemba effect: This is why hot water freezes faster than cold . In: Axel Springer SE (Ed.): Welt.de> kmpkt . March 1, 2018 ( welt.de [accessed June 14, 2019]).
- ↑ a b Heiner Grimm: Mpemba effect: hot water freezes faster than cold water? Calculation of the Mpemba effect and experimental investigation; Water evaporation. In: water. Heiner Grimm, accessed on June 14, 2019 .
- ↑ The “Clever” knowledge book: The scientific explanations from broadcast 39 ( Memento from July 1, 2010 in the Internet Archive ) sat1.de
- ↑ The little question: Why does warm water freeze faster than cold water? In: wdr5.de , January 21, 2010, 4:05 p.m.
- ^ The Mpemba effect: competition and resources. Royal Society of Chemistry
- ↑ How hot water is flash frozen. In: Süddeutsche Zeitung , January 8, 2014
